Linguistic variables play a vital role in several qualitative decision environments, in which decision-makers assume several feasible linguistic values or criteria instead of a single term for an alternative or variable. The motivation for the use of words or sentences instead of numbers is that linguistic classification and characterizations are generally less precise than numerical ones. In this research article, we encourage the fuzzy linguistic approach and introduce the novel concept known as m-polar fuzzy linguistic variable (mFLV) to increase the affluence of linguistic variables based on m-polar fuzzy (mF) approach. An mF set is an effective concept for interpreting uncertainty and fuzziness. The concept of mFLV is more versatile and sensible for dealing with real-life problems, when data comes from qualitative and multipolar information. We also introduce an mF linguistic ELECTRE-I approach to solve multiple-criteria decision-making (MCDM) and multiple-criteria group decision-making (MCGDM) problems, where the evaluation of the alternatives under suitable linguistic values are determined by the decision-makers. Furthermore, we validate the efficiency of our proposed technique by applying it to real-life examples, such as the salary analysis of companies and by selecting a corrupt country. Finally, we develop an algorithm of our proposed approach, present its flow chart, and generate computer programming code.

This study presents the theoretical investigation of a roll-over thin layer formation under the lubrication approximation theory. The set of differential equations derived by lubrication approximation is solved by the optimal homotopy asymptotic method (OHAM) to obtain precise expressions for pressure and velocity gradients. Critical quantities such as velocity, pressure gradient, and coating layer depth are numerically estimated. The impact of parameters affecting the coating and layer formation is revealed in detail. Results indicate that the transport properties of the higher-grade fluid play an essential role in regulating velocity, pressure, and the final coated region. Moreover, couple stress effects on the properties of fluid particles to be coated on roller-surface have also been studied.

In present learning, surface protection layer progression of a third-grade fluid (TGF) is examined. Fluid transport within the micro passage made by the firm bladehas beenpresented. Main system of equations of fluidity have been narrated and streamlined by means of lubrication approximation theory (LAT). Here, approximate solutions of velocity, pressure gradient, and coating depth have been presented. Results of coating and layer forming have been tabulated and discussed as well. It is observed that the transport properties of third-order fluid delivers an instrument to regulate flow velocity, pressure, and affect the final coated region.

This article introduces certain algebraic properties of generalized $({\tilde{h}}_1,{\tilde{h}}_2)$-pre-invex functions on ${\mathbb{R}}^{\mathsf{\aleph }}$$(0<\mathsf{\aleph }\le 1)$. A new fractal weighted integral identity is established and further employed to obtain several Ostrowski-type results in the fractal setting for functions whose first derivatives in the modulus belong to the generalized $({\tilde{h}}_1,{\tilde{h}}_2)$-pre-invex functions’s class. An illustrative example is presented to validate the theoretical findings. Moreover, applications of the main results are derived in connection with generalized random variables and various special means, highlighting the effectiveness and potential scope of the proposed approach.

The present investigation is related to the analysis of boundary layer (BL) flow of hydro-magnetic non-Newtonian Casson fluid (CF) which is fruitful for understanding the rheology of the fluid model for electrolyte application as a case study for Silicon Composite micro-porous electrode as sandwich channel with Soret-Dufour Effects for Lithium-Ion Batteries. The study of motile microorganisms (MMs) in the Casson flow field near the point of stagnation gives some insights over the porous stretchable heated surface to discuss the physical phenomenon and will be interesting to elucidate that how the movement of these microorganisms influence the flow field and how this phenomenon can be monitored by other pertinent factors. Viscosity is considered to be a linear function of temperature in which the fluid flow lodges or entertains the diffusion processes, due to the concentration gradients as well as temperature. The fascinating vivid features are presented to physically inspect the characteristics of flow; when the viscosity is a map of the change in temperature (or temp gradient), the velocity profile raises but it manages the temperature's fluid in the reverse direction. The approximate numerical values are combined for physical parameters. The integration of micro-porous electrodes made with silicon matrix to serve as sandwich channels experiencing Soret-Dufour phenomena alongside innovative micro-organism based electrolytes completes a breakthrough as far as lithium-ion battery technology is concerned. These enhancements pave the way for various high-demand applications opening up new frontiers in the field of energy storage.